ece340_final_fall2007_solution

ece340_final_fall2007_solution - FALL 2007 (12/11/07)...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FALL 2007 (12/11/07) ECE340(Engineerir_1g Systems Analysis) Name: EU Viv MOW"; 0 Final I. (15 pts) A system is defined by the input-output relationship ya) = x02) Is this system: a) (5 pts) Linear we 54‘ W = 7t. U?) 971(k): fifi‘y) c) (5 pts) Causal NO . (077575/‘3” "lé: ’2. (23/779142 (71/6; 9((9L) £40 owfffluf C/ePCMC/S (m A 7LW’¢ Mae/W9— 02¢ 49kt 7n/7LML, FALL 2007 (12/11/07) 2. a) (10 pts) Prove the following convolution theorem. (F is the Fourier transform) F{f_:x(T)/1(f— om} : X(f)-H(f) 973) x 4% k : 30° Mamet) dz too “217 ’L) :Smflab WM 7% 4244‘ .013 . "87,7770? "L77 {— , 0" 1(2)€ / of?) e) {41% FALL 2007 (12/11/07) 3. a) (10 pts) Prove the following duality theorem. (F is the Fourier transform) +) {filial % F{X(t)} = x(—f) 174) 7:1ij : £31 (U r: — ’ 5 log X1405“ M 0M ./fi b) (5 pts) Use the duality theorem to obtain the inverse Fourier transform of X (f) = 6(f — f0) . FALL 2007 (12/11/07) 4. (20 pts) Given the system. xm=clm ym 11(r) ——. Determine the output, Y ( f ) , for the following h(t) . a) (10 pts) h(t)= Eu: 6(t—nT) 9M XMJ—JW, WWMIL] \flfl : {ff Maj Ir: J n : —' ( —’ "f > 71%;: f T ( Mar «en Ewe/0 M I’M/64L wee/67444:) b) (10 pts) h(t)=f_l x(T)dT Me) : f 6506/" 5 “‘79 0: M55) 6,» (zwfflefi g/Jh‘fl J YQC) : (an)F/+ 2, JGE) ( £67m 47> a cm; fn M M 74w (Lama) FALL 2007 (12/1 l/07) 5. (10 pts) Given x[n] = cos[§n] u[n], M >1 m=l Determine the z—transform of x[n] and the region of convergence. M 1m): #671). (0} Z’n)uk(m) : go, (Lug/7n) LM“) 3 >([%') : (09(gn)_£—n /~ Cos/3'77)?" 6. (10 pts) Consider a quantizer with the following input—output relationship. N) FALL 2007 (12/11/07) 7. (15 pts) For the discrete-time system defined by the following difference equation yln] = x["] — xi" — 2l a) (5 pts) Determine the impulse response h[n]. hay) : glut). 5(l’l'1)/ b) (10 pts) Plot the magnitude response ofthe system, I H(e’"') |. HLe’n/a): ’1 é'Ha-w JPN BUO/ 73w. 7 a) é ) LJ ...
View Full Document

This note was uploaded on 10/06/2008 for the course ECE 340 taught by Professor Djordjevic during the Fall '08 term at University of Arizona- Tucson.

Page1 / 6

ece340_final_fall2007_solution - FALL 2007 (12/11/07)...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online